In many electronic applications, signals are represented and processed digitally. Digital words, or samples, represent the value of the signal at a regular time interval. This regular interval is often referred to as the sample rate, and is typically expressed in units of Hertz (Hz) representing the reciprocal of the sample interval time period. The signal thus represented can have no energy above half the sample rate; the frequency equal to half the sample rate is called the Nyquist frequency.
Digital sample rate conversion is used in many types of digital systems. For example, audio signals, such as might be generated in making recordings of music, are often processed digitally. The various pieces of equipment used to process and record the signals will not always operate at the same sampling frequency. As a result, it is often necessary that each piece of equipment accept a digital signal sampled at a first rate and then convert it to a digital signal with a second sampling rate before processing it. Of course, the information content of the signal must not be appreciably changed by the sample rate conversion or the sound quality of the signal will be degraded.
A very simple way to accomplish sample rate conversion is to simply drop out samples from the first signal. The output waveform thus has fewer samples per second and therefore has a lower sample rate. Assuming the Nyquist criterion is met in the output signal, it is an accurate representation of the same signal as the input. This process is referred to generally as “decimation.” It is limited, though, to situations in which the sampling rate of the input is an integer multiple of the sampling rate of the output.
A process called interpolation may be used when the sampling rate of the output is intended to be an integer multiple higher than the sampling rate of the input signal. In such an interpolation operation, an intermediate signal can be first produced by filling the time between samples of the input signal with samples which are arbitrarily assigned the value of zero. Such an intermediate signal is called a “zero-stuffed” signal. Because samples are added while the time span is kept the same, the zero-stuffed signal has a higher sampling rate than the input signal. The higher frequency zero-stuffed signal can be filtered in a digital interpolation filter that smoothes out the discontinuities caused by adding the extra samples. The result is a digital signal which has the same shape as the input signal, but contains more samples per second.
The processes of decimation and interpolation may be combined. For example, a circuit could decimate by a factor of D and interpolate by a factor of I. The resulting output would have a sampling rate in a ratio of I/D to the input sampling rate. Such a circuit is, however, limited to scaling the sampling rate by a rational number. More importantly, for a digital system, there are practical limits on the ranges of values for D and I. The decimation factor D can not be so large that the decimated signal no longer satisfies the Nyquist rate. Additionally, the interpolation factor I cannot be made arbitrarily large, because the required complexity of the interpolation filter increases as I gets larger (e.g., more taps). Moreover, it is presumed that at least one of the different clocks is essentially identical to the system clock (i.e., DSP clock), or at least related to it in a straightforward manner, such as by a factor of 2. Maintaining consistency between the different sample rate clocks in such situations places a burden on the accuracy and complexity of the hardware of the timing system.